Problem: Simplify the following expression: $ z = \dfrac{3}{10} - \dfrac{k + 7}{-4k} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-4k}{-4k}$ $ \dfrac{3}{10} \times \dfrac{-4k}{-4k} = \dfrac{-12k}{-40k} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{k + 7}{-4k} \times \dfrac{10}{10} = \dfrac{10k + 70}{-40k} $ Therefore $ z = \dfrac{-12k}{-40k} - \dfrac{10k + 70}{-40k} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-12k - (10k + 70) }{-40k} $ Distribute the negative sign: $z = \dfrac{-12k - 10k - 70}{-40k}$ $z = \dfrac{-22k - 70}{-40k}$ Simplify the expression by dividing the numerator and denominator by -2: $z = \dfrac{11k + 35}{20k}$